## GRE Math Tutorial

#### Intro

This is the problem in the probability and statistics asked frequenlty in the GRE-Quant section .In this problem ,we will have a look at the typical problem in the subject area which lays foundation concept for the further problems related to the probability which carries important portion in the GRE examination.

#### Sample Problem

1.There are 5 good and 6 damaged apples in a bag which look identical otherwise.You are told to take out the two apples simultaneously(not one by one ,if one by one the answer will be different). So what is the probability that you draw one good apple and one damaged apple.

5C2*6C2/11C2

5C11*6C1/11C1

5!*6!/11!

the data is not sufficient

5C1*6C1/11C2

#### Solution

1.First identify whether it is a combination problem or a permutation .This is the plcae where many of us get confused and commit the mistake .
In this case , does ‘the order in which the objects/or the subjects are arranged’ makes the outcomes different ?I mean does the order of two drawn apples like good-damaged or damaged=good are different or same.they are same ,so its a combination.

Lets take another example ,you are to make a password of 3 different digits out of 5 digits i.e. 0,1,2,3,4.Now ask yourself, does the order of the outcome matters . Lets say one outcome is 012 and another is 120 .Though they have the same objects /or subjects , the outcome are different password and the ‘ order’ matters .So this will be permutation.
2.After deciding the problem type,we confirm it is a combination problem.
If two apples are drawn from a bag of total 11( =5++6) ,they can be drawn in 11C2 ways .(C carries the meaning for mathematical operation.) 11C2= 11!/(2!*9!).=Total possible outcome
The desired outcome is the one good and one bad apple. so number of getting the result= 5C1*6C!.(As from 6 bad apples any one can be drawn in 6c1 ways , first..second..or sixth. so is the case for good apples .Since the the results are to happen at once .Multiply them .
Probability= 5C1*6C1/11C2
This is the basic but very crucial steps for learning the probability.I will present more in he upcoming tutorials .